Mixture models in haematology: a series of case studies

Two specific applications of finite mixture distributions in haematology include (1) the analysis of the distribution of red blood cell volumes to characterize and quantify alterations in erythrocyte subpopulations in anaemia and (2) the analysis of the distribution of transferrin saturation to estimate subpopulation parameters based on individual genotype for haemochromatosis. For these applications, we describe the comprehensive approach that was taken to distribution modeling. The choice of distributions and the number of mixture components to be fit were based upon theoretical and physiological considerations and a variety of additional statistical problems were considered. These included fitting mixtures of doubly-truncated data and evaluating model fit in the presence of extremely large sample sizes. As a result of the comprehensive approach taken to statistical problem solving in haematology, methods developed for analysis of red blood cell volume distributions have now been adopted by the International Council for Standardization in Haematology. Additionally, analysis of population transferrin saturation distributions from the white population of the USA has led to an independent estimate of the prevalence of homozygotes for haemochromatosis, confirming that the gene for haemochromatosis is common.